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On the influence of high priority customers on a generalized processor sharing queue

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Abstract
In this paper, we study a hybrid scheduling mechanism in discrete-time. This mechanism combines the well-known Generalized Processor Sharing (GPS) scheduling with strict priority. We assume three customer classes with one class having strict priority over the other classes, whereby each customer requires a single slot of service. The latter share the remaining bandwith according to GPS. This kind of scheduling is used in practice for the scheduling of jobs on a processor and in Quality of Service modules of telecommunication network devices. First, we derive a functional equation of the joint probability generating function of the queue contents. To explicitly solve the functional equation, we introduce a power series in the weight parameter of GPS. Subsequently, an iterative procedure is presented to calculate consecutive coefficients of the power series. Lastly, the approximation resulting from a truncation of the power series is verified with simulation results. We also propose rational approximations. We argue that the approximation performs well and is extremely suited to study these systems and their sensitivity in their parameters (scheduling weights, arrival rates, loads ...). This method provides a fast way to observe the behaviour of such type of systems avoiding time-consuming simulations.
Keywords
FLOW-CONTROL, Generalized Processor Sharing (GPS), DISCIPLINE, Priority, Queueing, Scheduling, Power series, INTEGRATED SERVICES NETWORKS

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MLA
Vanlerberghe, Jasper, et al. “On the Influence of High Priority Customers on a Generalized Processor Sharing Queue.” Lecture Notes in Computer Science, vol. 9081, Springer, 2015, pp. 203–16, doi:10.1007/978-3-319-18579-8_15.
APA
Vanlerberghe, J., Walraevens, J., Maertens, T., & Bruneel, H. (2015). On the influence of high priority customers on a generalized processor sharing queue. Lecture Notes in Computer Science, 9081, 203–216. https://doi.org/10.1007/978-3-319-18579-8_15
Chicago author-date
Vanlerberghe, Jasper, Joris Walraevens, Tom Maertens, and Herwig Bruneel. 2015. “On the Influence of High Priority Customers on a Generalized Processor Sharing Queue.” In Lecture Notes in Computer Science, 9081:203–16. Springer. https://doi.org/10.1007/978-3-319-18579-8_15.
Chicago author-date (all authors)
Vanlerberghe, Jasper, Joris Walraevens, Tom Maertens, and Herwig Bruneel. 2015. “On the Influence of High Priority Customers on a Generalized Processor Sharing Queue.” In Lecture Notes in Computer Science, 9081:203–216. Springer. doi:10.1007/978-3-319-18579-8_15.
Vancouver
1.
Vanlerberghe J, Walraevens J, Maertens T, Bruneel H. On the influence of high priority customers on a generalized processor sharing queue. In: Lecture Notes in Computer Science. Springer; 2015. p. 203–16.
IEEE
[1]
J. Vanlerberghe, J. Walraevens, T. Maertens, and H. Bruneel, “On the influence of high priority customers on a generalized processor sharing queue,” in Lecture Notes in Computer Science, Albena, Bulgaria, 2015, vol. 9081, pp. 203–216.
@inproceedings{6716027,
  abstract     = {{In this paper, we study a hybrid scheduling mechanism in discrete-time. This mechanism combines the well-known Generalized Processor Sharing (GPS) scheduling with strict priority. We assume three customer classes with one class having strict priority over the other classes, whereby each customer requires a single slot of service. The latter share the remaining bandwith according to GPS. This kind of scheduling is used in practice for the scheduling of jobs on a processor and in Quality of Service modules of telecommunication network devices. First, we derive a functional equation of the joint probability generating function of the queue contents. To explicitly solve the functional equation, we introduce a power series in the weight parameter of GPS. Subsequently, an iterative procedure is presented to calculate consecutive coefficients of the power series. Lastly, the approximation resulting from a truncation of the power series is verified with simulation results. We also propose rational approximations. We argue that the approximation performs well and is extremely suited to study these systems and their sensitivity in their parameters (scheduling weights, arrival rates, loads ...). This method provides a fast way to observe the behaviour of such type of systems avoiding time-consuming simulations.}},
  author       = {{Vanlerberghe, Jasper and Walraevens, Joris and Maertens, Tom and Bruneel, Herwig}},
  booktitle    = {{Lecture Notes in Computer Science}},
  isbn         = {{978-3-319-18579-8}},
  issn         = {{0302-9743}},
  keywords     = {{FLOW-CONTROL,Generalized Processor Sharing (GPS),DISCIPLINE,Priority,Queueing,Scheduling,Power series,INTEGRATED SERVICES NETWORKS}},
  language     = {{eng}},
  location     = {{Albena, Bulgaria}},
  pages        = {{203--216}},
  publisher    = {{Springer}},
  title        = {{On the influence of high priority customers on a generalized processor sharing queue}},
  url          = {{http://doi.org/10.1007/978-3-319-18579-8_15}},
  volume       = {{9081}},
  year         = {{2015}},
}

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